Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, p. 1111-1132
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears to be in good agreement with the theory.
DOI : https://doi.org/10.1051/m2an:2003008
Classification:  35K60,  65N12
Keywords: oblique derivative boundary problem, finite difference scheme, heat equation, Burgers equation
@article{M2AN_2002__36_6_1111_0,
     author = {Mehats, Florian},
     title = {Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {6},
     year = {2002},
     pages = {1111-1132},
     doi = {10.1051/m2an:2003008},
     zbl = {1060.65100},
     mrnumber = {1958661},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_6_1111_0}
}
Mehats, Florian. Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, pp. 1111-1132. doi : 10.1051/m2an:2003008. http://www.numdam.org/item/M2AN_2002__36_6_1111_0/

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